This week’s mediocre financial showing by Chrysler should be more than offset by its cross-town rival, General Motors, at least if signals sent by two of its top executives are any indication.

Former Wall Street whiz kid and now GM Vice Chairman Steve Girsky has suggested observers “will be encouraged” by the automaker’s second-quarter numbers, which are expected Thursday. They’ll need to be very impressed, in fact, if Girsky’s boss, GM Chairman and CEO Ed Whitacre, is to pull off a miracle in the coming months.

Speaking at an industry confab in Traverse City, Mich., last week, “Big Ed,” the former chairman of AT&T and the government’s choice to take over GM after last year’s bankruptcy, sent similarly positive signals about the April-June earnings. That’s one of the benefits of being a privately held company. Such comments would be off-limits were the automaker publicly traded and subject to strict SEC guidelines.

But speaking with his trademark Texas twang, Whitacre made it clear he’d be happy to have to live up to the rules for Wall Street if it allowed him to get the government out of his boardroom. The GM chairman said that staging a much-anticipated initial public offering of stock, or IPO, is “No. 1 on our list.”

CNBC and Reuters reported Wednesday the automaker could file as soon as Friday. Reuters, citing an anonomous sources, said the IPO would attempt to raise $10 billion and likely happen before Thanksgiving — but the timing had nothing to do with midterm elections.

Even before he abandoned the “acting” modifier to his role as chief executive officer early this year, Whitacre has been cagey about setting a hard date for the IPO. That is no surprise, say analysts like Joe Phillippi, of AutoTrends Consulting, who notes that GM will have a serious challenge convincing potential investors to pony up the billions of dollars it will take to make for a successful re-emergence onto the NYSE’s Big Board.

If the quarterly results are as positive as Whitacre is hinting, that could build momentum for the stock sale. The oddsmakers are targeting a date of sometime just before the upcoming midterm congressional elections, which would fall in line with what the Obama administration has been pressing for.

And the administration has plenty of clout considering it holds a 60.8% stake in post-Chapter 11 GM, with the rest of the shares divided up among the Canadian government, the United Auto Workers Union’s VEBA program and former GM bondholders.

The consensus is that this could be the biggest IPO ever, even larger than the $19.8 billion raised by Visa Inc.’s public offering in March 2008.

There are several key factors that will determine the outcome. For one thing, will GM and the White House agree to sell all or just some of the Treasury’s holdings? When rumors of the IPO began circulating, last month, most “knowledgeable insiders” were betting that only about a quarter of the government’s holdings would be immediately auctioned off, in order to ensure GM didn’t overwhelm the market — which could drive down bidding.

There is the issue of the economy as well, and the latest spate of bad news hasn't exactly encouraged investors, especially those being asked to bet on the revival of what was long the largest automaker in the world. On the other hand, a strong second-quarter report could prove to the world that GM has really accomplished what it promised with its court-ordered reorganization.

During the middle of the last decade, in some of the best years the U.S. auto industry has ever experienced, the automaker racked up billions of dollars in losses. Now, even in one of the worst years the market has seen since the Great Depression, GM is moving solidly into the black. And with its increasing focus on foreign markets, particularly booming China, Whitacre & Co. insist the future is only brighter.

Which may be why the CEO also was broadly hinting last week that the entire government share, all 61 percent, could be offered up in the GM IPO. But the economics are daunting. The Treasury shelled out $40.7 billion for its 358.7 million shares. And if you have a calculator handy you can confirm that works out to $113 a share — even more when you factor in the cut the IPO’s underwriters will take.

Considering that Ford, widely praised as the current domestic industry success story, is trading at barely a tenth of that — though it also has 3.4 billion shares outstanding — it will be a stretch for GM to pull it off.

So, why would Whitacre be willing to take the risk? Consider another telling remark he made in Traverse City: “We don’t like this label of ‘Government Motors.’ It turns customers off and it turns us off.”

There’s a big irony here. Though Whitacre was appointed by the current Democratic President Barack Obama, he has a history with the Republican Party and was one of President George W. Bush’s top fundraisers. Yet his company, GM, is the target of vehement criticism from the GOP’s most conservative wing, with Rush Limbaugh and other talk radio hosts often asking listeners to boycott its products.

While analysts downplay the impact on sales, the Government Motors label clearly hasn’t helped, even among less politicized buyers. Research by the consulting firm CNW Marketing, on the other hand, suggests that Ford — the only one of Detroit’s Big Three to reject a federal bailout — has reaped significant rewards for its decision to tough out the Great Recession.

Labels don’t mean much to Wall Street unless they have a significant impact on sales and earnings. With GM showing solid momentum, Whitacre insists “the appetite in the marketplace is going to be really good for GM stock.”

The White House better hope he’s right — and that the second-quarter GM numbers live up to expectations.